1 13. (a) Prove: If A is invertible, then det(A-1) = A %3D det(A) (b) Prove: If A is invertible, then adj(A) is invertible and [adj(A-!)] = Za4- = adj(A). %3D det(A-) (Hint: you may use part (a) to prove part (6) of this proof)

Q: (15) If X-exp(1), then (a) 2X-exp(2) (c) 2x~exp (¹) O a O b O C Od (b) 2X-X² (2) (d) 2X-G(2,1) is

A: Given that X~exp(1) then  We have to find 2X follows which distribution:

Q: 2) Let A be 51 4 1 Compute: -1 T A (i) A² (ii) è¹_ (iii) (4²)`¹ (iv) (4²¹)² (v) A A² tr(AA¹) (vi)

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: (a) Let A € R²x2, Prove that (Write A(ax+By) =aAx+ Ay for all a, ß € R, x, y € R². ^-[22][3)--[G] ],…

A:

Q: T -2 4 f(x) g(r)|h(r) 5 4 9 2 -3

A:

Q: can someone explain what is going on in this part of the problem. Is this the method of…

A: It is a method to find the particular integral of the Ordinary differential equation.Here, it is…

Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (z² + 3z – 5)/2³ (3) (2z…

A: 3. Given function is 2z+1zz3-5.

Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (z² + 3z – 5)/2³ (3)…

A:

Q: -7 3 5 Suppose [v]B₁ - [¯? ]· ¹ B³,₁ - { [ 2 ] [ ³ ]} and B₂ = {[2] [3]}, = = 5 [V] B₂ = find [v]…

A: Given that

Q: Orthonormalize [1, t, t²} in P₂(R) with (p, q) = p(0)q(0) + p(1)q(1) +p(2)q(2) }

A:

Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (z² + 3z – 5)/2³ (3)…

A:

Q: If f is invertible and f( – 1) = 11, then f-'(11) = and (f( – 1))-1 |

A: Given. f(x) is an invertible function. f(-1) = 11

Q: k ak ak a-1,a +1 (-1)* 1/½(-1)*+1 kak 4), a +1 a- (ak + b)(n) (ak+b)(n+1) a(n+1)

A: ∆ak= ak+1-ak      = ak(a-1) therefore anti difference of ak=ak/(a-1)

Q: The Boolean function F(x, y) = x'y + xy' + (x+y')x can be simplified to:

A:

Q: Find the residues of the followings functions at z = 0: (1) (z² + 1)/z (2) (2² + 3z – 5)/z3 (3) (2z…

A:

Q: If the invertible function f (x) satisfies f (12) = 6, then which of the following statements is…

A: Option C is correct option.